By using a recently released version of the CFD(Computational Fluid Dynamics) software package FLUENT with an advanced RNG(ReNormalization Group) turbulence model, this study will enable us to numerically simulate unsteady turbulent flow in the vicinity of an artificial heart valve. We will then compare the random, small scale turbulent structures with the orderly, large scale flow structures as those induced by `vortex shedding', and estimate the actual Reynolds stress tensor, which is believed to be one of the major mechanical factors contributing to blood cell damage in artificial hearts.